/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: a__U11(tt(),N,X,XS) -> a__U12(a__splitAt(mark(N),mark(XS)),X) 2: a__U12(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS)) 3: a__afterNth(N,XS) -> a__snd(a__splitAt(mark(N),mark(XS))) 4: a__and(tt(),X) -> mark(X) 5: a__fst(pair(X,Y)) -> mark(X) 6: a__head(cons(N,XS)) -> mark(N) 7: a__natsFrom(N) -> cons(mark(N),natsFrom(s(N))) 8: a__sel(N,XS) -> a__head(a__afterNth(mark(N),mark(XS))) 9: a__snd(pair(X,Y)) -> mark(Y) 10: a__splitAt(0(),XS) -> pair(nil(),mark(XS)) 11: a__splitAt(s(N),cons(X,XS)) -> a__U11(tt(),N,X,XS) 12: a__tail(cons(N,XS)) -> mark(XS) 13: a__take(N,XS) -> a__fst(a__splitAt(mark(N),mark(XS))) 14: mark(U11(X1,X2,X3,X4)) -> a__U11(mark(X1),X2,X3,X4) 15: mark(U12(X1,X2)) -> a__U12(mark(X1),X2) 16: mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2)) 17: mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2)) 18: mark(snd(X)) -> a__snd(mark(X)) 19: mark(and(X1,X2)) -> a__and(mark(X1),X2) 20: mark(fst(X)) -> a__fst(mark(X)) 21: mark(head(X)) -> a__head(mark(X)) 22: mark(natsFrom(X)) -> a__natsFrom(mark(X)) 23: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) 24: mark(tail(X)) -> a__tail(mark(X)) 25: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) 26: mark(tt()) -> tt() 27: mark(pair(X1,X2)) -> pair(mark(X1),mark(X2)) 28: mark(cons(X1,X2)) -> cons(mark(X1),X2) 29: mark(s(X)) -> s(mark(X)) 30: mark(0()) -> 0() 31: mark(nil()) -> nil() 32: a__U11(X1,X2,X3,X4) -> U11(X1,X2,X3,X4) 33: a__U12(X1,X2) -> U12(X1,X2) 34: a__splitAt(X1,X2) -> splitAt(X1,X2) 35: a__afterNth(X1,X2) -> afterNth(X1,X2) 36: a__snd(X) -> snd(X) 37: a__and(X1,X2) -> and(X1,X2) 38: a__fst(X) -> fst(X) 39: a__head(X) -> head(X) 40: a__natsFrom(X) -> natsFrom(X) 41: a__sel(X1,X2) -> sel(X1,X2) 42: a__tail(X) -> tail(X) 43: a__take(X1,X2) -> take(X1,X2) Number of strict rules: 43 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__U12(pair(YS,ZS),X) -> #mark(X) #2: #a__U12(pair(YS,ZS),X) -> #mark(ZS) #3: #mark(s(X)) -> #mark(X) #4: #a__head(cons(N,XS)) -> #mark(N) #5: #a__take(N,XS) -> #a__fst(a__splitAt(mark(N),mark(XS))) #6: #a__take(N,XS) -> #a__splitAt(mark(N),mark(XS)) #7: #a__take(N,XS) -> #mark(N) #8: #a__take(N,XS) -> #mark(XS) #9: #a__snd(pair(X,Y)) -> #mark(Y) #10: #a__splitAt(s(N),cons(X,XS)) -> #a__U11(tt(),N,X,XS) #11: #mark(tail(X)) -> #a__tail(mark(X)) #12: #mark(tail(X)) -> #mark(X) #13: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2)) #14: #mark(sel(X1,X2)) -> #mark(X1) #15: #mark(sel(X1,X2)) -> #mark(X2) #16: #a__tail(cons(N,XS)) -> #mark(XS) #17: #mark(U11(X1,X2,X3,X4)) -> #a__U11(mark(X1),X2,X3,X4) #18: #mark(U11(X1,X2,X3,X4)) -> #mark(X1) #19: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2)) #20: #mark(take(X1,X2)) -> #mark(X1) #21: #mark(take(X1,X2)) -> #mark(X2) #22: #mark(fst(X)) -> #a__fst(mark(X)) #23: #mark(fst(X)) -> #mark(X) #24: #a__natsFrom(N) -> #mark(N) #25: #a__splitAt(0(),XS) -> #mark(XS) #26: #a__fst(pair(X,Y)) -> #mark(X) #27: #mark(cons(X1,X2)) -> #mark(X1) #28: #mark(natsFrom(X)) -> #a__natsFrom(mark(X)) #29: #mark(natsFrom(X)) -> #mark(X) #30: #mark(pair(X1,X2)) -> #mark(X1) #31: #mark(pair(X1,X2)) -> #mark(X2) #32: #mark(afterNth(X1,X2)) -> #a__afterNth(mark(X1),mark(X2)) #33: #mark(afterNth(X1,X2)) -> #mark(X1) #34: #mark(afterNth(X1,X2)) -> #mark(X2) #35: #mark(and(X1,X2)) -> #a__and(mark(X1),X2) #36: #mark(and(X1,X2)) -> #mark(X1) #37: #mark(head(X)) -> #a__head(mark(X)) #38: #mark(head(X)) -> #mark(X) #39: #mark(splitAt(X1,X2)) -> #a__splitAt(mark(X1),mark(X2)) #40: #mark(splitAt(X1,X2)) -> #mark(X1) #41: #mark(splitAt(X1,X2)) -> #mark(X2) #42: #a__afterNth(N,XS) -> #a__snd(a__splitAt(mark(N),mark(XS))) #43: #a__afterNth(N,XS) -> #a__splitAt(mark(N),mark(XS)) #44: #a__afterNth(N,XS) -> #mark(N) #45: #a__afterNth(N,XS) -> #mark(XS) #46: #a__U11(tt(),N,X,XS) -> #a__U12(a__splitAt(mark(N),mark(XS)),X) #47: #a__U11(tt(),N,X,XS) -> #a__splitAt(mark(N),mark(XS)) #48: #a__U11(tt(),N,X,XS) -> #mark(N) #49: #a__U11(tt(),N,X,XS) -> #mark(XS) #50: #a__sel(N,XS) -> #a__head(a__afterNth(mark(N),mark(XS))) #51: #a__sel(N,XS) -> #a__afterNth(mark(N),mark(XS)) #52: #a__sel(N,XS) -> #mark(N) #53: #a__sel(N,XS) -> #mark(XS) #54: #mark(U12(X1,X2)) -> #a__U12(mark(X1),X2) #55: #mark(U12(X1,X2)) -> #mark(X1) #56: #a__and(tt(),X) -> #mark(X) #57: #mark(snd(X)) -> #a__snd(mark(X)) #58: #mark(snd(X)) -> #mark(X) Number of SCCs: 1, DPs: 58 SCC { #1..58 } POLO(Sum)... POLO(max)... succeeded. U11 w: max(x1 + 8, x2 + 7, x3 + 11, x4 + 9) s w: x1 #a__head w: x1 + 9 #a__natsFrom w: x1 + 9 #a__snd w: x1 + 1 a__afterNth w: max(x1 + 11, x2 + 10) take w: max(x1 + 9, x2 + 10) and w: max(x1 + 3, x2 + 2) pair w: max(x1 + 8, x2 + 9) fst w: x1 + 1 natsFrom w: x1 + 2 a__snd w: x1 + 1 splitAt w: max(x1 + 7, x2 + 9) #a__U11 w: max(x1 + 12, x2 + 11, x3 + 14, x4 + 12) #a__take w: max(x1 + 13, x2 + 13) U12 w: max(x1, x2 + 11) #a__U12 w: max(x1 + 1, x2 + 9) a__fst w: x1 + 1 a__natsFrom w: x1 + 2 tail w: x1 + 2 #mark w: x1 + 8 0 w: 1 #a__and w: max(x2 + 9) sel w: max(x1 + 17, x2 + 14) afterNth w: max(x1 + 11, x2 + 10) nil w: 1 a__splitAt w: max(x1 + 7, x2 + 9) #a__sel w: max(x1 + 21, x2 + 21) mark w: x1 a__U11 w: max(x1 + 8, x2 + 7, x3 + 11, x4 + 9) a__sel w: max(x1 + 17, x2 + 14) a__U12 w: max(x1, x2 + 11) head w: x1 + 4 #a__afterNth w: max(x1 + 13, x2 + 13) #a__splitAt w: max(x1 + 11, x2 + 12) cons w: max(x1 + 2, x2) snd w: x1 + 1 a__take w: max(x1 + 9, x2 + 10) tt w: 2 #a__fst w: x1 + 1 a__and w: max(x1 + 3, x2 + 2) a__tail w: x1 + 2 #a__tail w: x1 + 9 a__head w: x1 + 4 USABLE RULES: { 1..43 } Removed DPs: #1 #2 #4..9 #11..46 #48..54 #56..58 Number of SCCs: 2, DPs: 4 SCC { #3 #55 } POLO(Sum)... succeeded. U11 w: x1 + x3 + x4 + 5 s w: x1 + 1 #a__head w: 1 #a__natsFrom w: 1 #a__snd w: 1 a__afterNth w: 2 take w: 1 and w: 1 pair w: 3 fst w: 1 natsFrom w: 4 a__snd w: 2 splitAt w: x1 + x2 + 4 #a__U11 w: 0 #a__take w: 1 U12 w: x1 + x2 + 1 #a__U12 w: 0 a__fst w: 4 a__natsFrom w: 3 tail w: x1 + 4 #mark w: x1 + 1 0 w: 3 #a__and w: 1 sel w: 2 afterNth w: 2 nil w: 0 a__splitAt w: 3 #a__sel w: 1 mark w: 2 a__U11 w: x2 + 4 a__sel w: x1 + 2 a__U12 w: 0 head w: 4 #a__afterNth w: 1 #a__splitAt w: 0 cons w: 1 snd w: x1 + 3 a__take w: 3 tt w: 0 #a__fst w: 1 a__and w: x2 + 1 a__tail w: 3 #a__tail w: 2 a__head w: 3 USABLE RULES: { } Removed DPs: #3 #55 Number of SCCs: 1, DPs: 2 SCC { #10 #47 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. U11 s: [3,2] p: 6 w: max(x2 + 1, x3 + 8, x4 + 9) s s: [1] p: 10 w: x1 #a__head s: [] p: 0 w: 0 #a__natsFrom s: [] p: 0 w: 1 #a__snd s: [] p: 0 w: 1 a__afterNth s: [] p: 7 w: x1 + x2 + 10 take s: [] p: 11 w: x1 + x2 + 12 and s: [] p: 0 w: x2 + 1 pair s: [] p: 0 w: max(x1 + 5, x2 + 4) fst s: [] p: 10 w: x1 + 2 natsFrom s: [] p: 12 w: x1 + 4 a__snd s: 1 splitAt s: [] p: 7 w: max(x1 + 1, x2 + 9) #a__U11 s: [2] p: 10 w: max(x2) #a__take s: [] p: 0 w: x1 + 1 U12 s: [] p: 6 w: max(x1, x2 + 8) #a__U12 s: [2,1] p: 0 w: x1 + x2 a__fst s: [] p: 10 w: x1 + 2 a__natsFrom s: [] p: 12 w: x1 + 4 tail s: [] p: 7 w: x1 + 1 #mark s: [] p: 0 w: 1 0 s: [] p: 10 w: 1 #a__and s: [] p: 0 w: 0 sel s: [] p: 8 w: x1 + x2 + 12 afterNth s: [] p: 7 w: x1 + x2 + 10 nil s: [] p: 11 w: 2 a__splitAt s: [] p: 7 w: max(x1 + 1, x2 + 9) #a__sel s: [] p: 0 w: x1 mark s: 1 a__U11 s: [3,2] p: 6 w: max(x2 + 1, x3 + 8, x4 + 9) a__sel s: [] p: 8 w: x1 + x2 + 12 a__U12 s: [] p: 6 w: max(x1, x2 + 8) head s: [] p: 10 w: x1 + 1 #a__afterNth s: [] p: 0 w: x2 #a__splitAt s: 1 cons s: [] p: 12 w: max(x1 + 3, x2) snd s: 1 a__take s: [] p: 11 w: x1 + x2 + 12 tt s: [] p: 11 w: 2 #a__fst s: [] p: 0 w: 1 a__and s: [] p: 0 w: x2 + 1 a__tail s: [] p: 7 w: x1 + 1 #a__tail s: [] p: 0 w: 0 a__head s: [] p: 10 w: x1 + 1 USABLE RULES: { 1..43 } Removed DPs: #47 Number of SCCs: 0, DPs: 0